Techno Press
You logged in as Techno Press

Coupled Systems Mechanics
  Volume 4, Number 1, March 2015, pages 1-18
DOI: http://dx.doi.org/10.12989/csm.2015.4.1.001
 


Localized particle boundary condition enforcements for the state-based peridynamics
C.T. Wuand Bo Ren

 
Abstract
    The state-based peridynamics is considered a nonlocal method in which the equations of motion utilize integral form as opposed to the partial differential equations in the classical continuum mechanics. As a result, the enforcement of boundary conditions in solid mechanics analyses cannot follow the standard way as in a classical continuum theory. In this paper, a new approach for the boundary condition enforcement in the state-based peridynamic formulation is presented. The new method is first formulated based on a convex kernel approximation to restore the Kronecker-delta property on the boundary in 1-D case. The convex kernel approximation is further localized near the boundary to meet the condition that recovers the correct boundary particle forces. The new formulation is extended to the two-dimensional problem and is shown to reserve the conservation of linear momentum and angular momentum. Three numerical benchmarks are provided to demonstrate the effectiveness and accuracy of the proposed approach.
 
Key Words
    state-based; peridynamics; convex kernel approximation; boundary condition
 
Address
C.T. Wu: Livermore Software Technology Corporation, 7374 Las Positas Road, Livermore, CA 94551, USA
Bo Ren: Department of Civil and Environmental Engineering, University of California, Berkeley CA 94720, USA
 

Techno-Press: Publishers of international journals and conference proceedings.       Copyright © 2020 Techno Press
P.O. Box 33, Yuseong, Daejeon 305-600 Korea, Tel: +82-42-828-7996, Fax : +82-42-828-7997, Email: info@techno-press.com